Extreme precipitation can often cause serious hazards such as flooding and landslide. Both pose a threat to human lives and lead to substantial economic loss. It is crucial to develop a reliable weather forecasting system that can predict such extreme events to mitigate the effect of heavy precipitation and increase resilience to these hazards. Numerical Weather Prediction (NWP) models play the dominant role in the field of weather forecasting. However, due to their long computational time, these models had limited utility in predicting weather conditions in the following several hours. This gap is filled by nowcasting, an observation-based method that uses the current state of the atmosphere to forecast future weather conditions for several hours. Operational nowcasting systems typically apply extrapolation algorithms to rainfall radar observations based on simple physics assumptions. However, the physics constraints also limit the performance, and the methods can hardly capture non-linear patterns in the radar observations. Besides the conventional methods, deep learning models have started to play an essential role in this field. Recent works have shown the promising potential of using deep learning models to tackle the nowcasting task, which is also this thesis's focus. The thesis work mainly studied in two directions: the development of novel deep generative models for precipitation nowcasting and the application of statistical approaches for better modeling and prediction of extreme events. For the first direction, our proposed model is inspired by recently developed deep learning models from the field of visual synthesis. The model makes use of a two-stage structure: the first stage is a Vector Quantization Variational Autoencoder (VQ-VAE) which compresses the original high-resolution radar observations into a low-dimensional latent space. The second stage works in this latent space. It contains an autoregressive Transformer that models the probabilistic distribution of latent space data. The trained Transformer can predict the latent space representation of future frames. For better modeling and prediction of extreme events, Extreme Value Loss (EVL) is proposed and incorporated with the autoregressive Transformer. The loss function aims at penalizing predicting extreme cases as non-extreme and predicting non-extreme cases as extreme in order to solve the high imbalance between extreme and normal precipitation data. Our results show that the proposed model shows comparable performance with the state-of-the-art conventional method and other deep learning nowcasting models. The proposed EVL has also been shown to improve the overall performance and accuracy in predicting extreme events.